The Geometry of Physics: An Introduction, Revised Edition (Softcover)

Condition

VERY GOOD: This book is in very good condition, showing a few signs of use and wear (namely, slightly bent cover and page corners). The pages are free of writing.

Product Details

Continued from the back cover: "Included are discussions of analytical and fluid dynamics, electromagnetism (in flat and curved spaces), thermodynamics, elasticity theory, the geometry and topology of Kirchhoff's electric circuit laws, soap films, special and general relativity, the Dirac operator and spinors, and gauge fields, including Yang-Mills, the Aharonov-Bohm effect, Berry phase, and instanton winding numbers. Before discussing abstract notions of differential geometry, geometric intuition is developed through a rather extensive introduction to the study of surfaces in ordinary space; consequently, the book should be of interest also to mathematics students.

"This book will be useful to graduate and advanced undergraduate students of physics, engineering and mathematics. It can be used as a course text or for self study.

"This revised printing contains new corrections and additions and also a new Appendix B, Harmonic Chains and Kirchhoff's Circuit Laws. This appendix, using matrices and linear algebra, gives a concrete and elementary version of cohomology and the Hodge theory of Chapter 14. This yields a systematic 'geometrical' description of the Kirchhoff circuit laws (where currents are chains, voltages are cochains, and the 'admittance' is the laplacian) and their applications to direct current circuits, first considered from roughly this viewpoint by Hermann Weyl."

BRIEF CONTENTS

I. Manifolds, Tensors, and Exterior Forms

1. Manifolds and Vector Fields
2. Tensors and Exterior Forms
3. Integration of Differential Forms
4. The Lie Derivative
5. The Poincaré Lemma and Potentials
6. Holonomic and Nonholonomic Constraints

II. Geometry and Topology

7. R³ and Minkowski Space
8. The Geometry of Surfaces in R³
9. Covariant Differentiation and Curvature
10. Geodesics
11. Relativity, Tensors, and Curvature
12. Curvature and Topology: Synge's Theorem
13. Betti Numbers and De Rham's Theorem
14. Harmonic Forms

III. Lie Groups, Bundles, and Chern Forms

15. Lie Groups
16. Vector Bundles in Geometry and Physics
17. Fiber Bundles, Gauss-Bonnet, and Topological Quantization
18. Connections and Associated Bundles
19. The Dirac Equation
20. Yang-Mills Fields
21. Betti Numbers and Covering Spaces
22. Chern Forms and Homotopy Groups

Appendices

1. Forms in Continuum Mechanics
2. Harmonic Chains and Kirchhoff's Circuit Laws

The book concludes with References and Index.